Information Technology Reference
In-Depth Information
7.2.2
Conditions of concept acquisition
In concept acquisition observed statements facts
F
can be viewed as implications
of the form:
F
: {
e
ik
K
i
}
i
Ӥ
I
(7.1)
::
>
where
e
ik
(training event of
K
i
) is symbol description of number
k
instance of
concept
K
i
. Conceptual predicate
K
i
,
i
is suffix set of
K
i
.
e
ik
::>
K
i
means that
“all events in accordance with description
e
ik
can be asserted to be instances of
concept
K
i
”. The inductive hypothese
H
seeked out by learning program can be
depicted by concept recognition rule set. Its form is as following:
H: {
D
i
K
i
}
i
Ӥ
I
(7.2)
::
>
where
D
i
is the description of concept
K
i
i.e. expression
D
i
is logic conclusion of
K
i
.
events, which can be asserted as an instance of concept
Using
E
i
to represent all description of training events in concept
K
i
(
i
∈
I ),
|
1
F
. In order to
according to the definition of inductive assertionit must hold
H
let
D
i
become the description of concept
K
i
using expression (7.1) and (7.2) to
replace
respectively, the following condition must hold:
∀
i
∈
I (E
i
⇒
D
i
)
H
and
F
(7.3)
i.e. all training events of
D
i
. If every event only
belongs to one concept, the following condition also holds:
∀
K
i
must be in accordance with
E
i
) if
i
≠
j
(7.4)
i,j
∈
I
(
D
i
⇒
∼
it means training events of every concept
Condition (7.3) is referred to as integral condition. Condition (7.4) is referred to
as consistence condition. As accepted by concept recognition rule, inductive
assertion must meet these two conditions, so that the integral and consistence can
be assured. Integral condition and consistence condition provide logical
foundation for conceptual algorithm of instance learning.
Description of a kind of objects is a expression satisfying integral condition,
or conjunction of these expressions. This kind of description judges given
category from all possible categories. Difference description of an object
category is a expression satisfying integral condition, or disjunction of these
expressions. Its objective is to label given category in few other categories.
The main interest of knowledge acquisition lies in symbol description
orirnted reasoning. This description should be easily understood, and easily
applied when generating intelligence model which represents its information.
Therefore, description generated by inductive reasoning should be similar to
human knowledge representation.
In inductive learning classification, a guiding principle is choosing language
type of inductive learning such as some kind of definitive form or similar concept
K
i
(j
≠
i
) are not in accordance with
D
i
.
